With an equivalent anchoring energy formula for grating surface and elastic theory, a hybrid aligned nematic (HAN) liquid crystal cell proposed by Bryan-Brown et al is studied. Equations and boundary conditions for tilt angle and twist angle of director are obtained with variation theory. Tilt angle and twist angle of director with applied voltage at certain δ/λ are calculated with finite-difference iterative method. Electro-optical effect of liquid crystal cells is investigated with Jones matrix method. It depends on geometrical parameters of the grating surface, pitch λ and amplitude δ.

With elastic theory of liquid crystal,we investigate bulk flexoelectric effect in a nematic liquid crystal(NLC) cell with applied voltage.The differential equation of director tilt angle θ is obtained by the variation theory. The distributions of director in a strong anchoring planar aligned cell and in a hybrid aligned nematic(HAN) cell are calculated. The transmittance characteristic of these liquid crystal cells is obtained with Jones matrix method.Influence of bulk flexoelectric effect on the distribution of director and characteristic transmittance of liquid crystal cells are analyzed.

Some important physical effects appear due to short range order in nematic liquid crystals. On the basis of the cell theory, new numerical method is presented, which are used to calculate these effects.We do not use ann functional expansions but we obtain accurate orientational distribution functions by solving the equation of equilibrium state, using an iterative method. Then various physical quantities can be calculated. The accurate numerical results of order parameter at phase transition and entropy change etc. are given.